When the reliability analysis of the mechanical products with high nonlinearity and time-consuming response is carried out, there will be the problems of low precision and huge computation using the traditional reliability methods. To solve these issues, the active learning reliability methods have been paid much attention in recent years. It is the key to choose an efficient learning function (such as U, EFF, and ERF). The aim of this study is to further decrease the computation and improve the accuracy of the reliability analysis. Inspired from these learning functions, a new point-selected learning function (called HPF) is proposed to update DOE, and a new point is sequentially added step by step to the DOE. The proposed learning function can consider the features like the sampling density, the probability to be wrongly predicted, and the local and global uncertainty close to the limit state. Based on the stochastic property of the Kriging model, the analytic expression of HPF is deduced by averaging a hybrid indicator throughout the real space. The efficiency of the proposed method is validated by two explicit examples. Finally, the proposed method is applied to the mechanical reliability analysis (involving time-consuming and nonlinear response). By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision.